From a ghosts exist point of view.. Yes, haunted objects exist. There's tons of stories out there about ghosts popping up when their remains are disturbed or sticking around till their remains are properly buried. Bad luck or weird stuff happening after taking something home from a haunted place, cursed gems, haunt stories following objects like bits from the Titanic or something dug up from a war field.

From a personal point of view, I'm not sure. I've known some people personally that have claimed weird or haunted object stories. Some of them, yeah, I doubt it. Some of them I'm not too sure if I should doubt their word.

From a ghosts don't exist point of view. No, no haunted objects. But I believe that objects can sometimes store or hold energy, and that might cause the appearance of haunting.